Mixing angles of quarks and leptons in quantum field theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2) _L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2) _f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns on the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ ₂₃ is maximal and tan (2θ ₁₂)=2. The Cabibbo angle fulfills the condition tan (2θ _c )=1/2 and θ ₁₂ for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θ _c +θ ₁₂=π/4. θ ₁₃=±5.7⋅10⁻³ are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly broken symmetry of the Standard Model is outlined.     

Topological characterization of leptons,quarks and hadrons

Electromagnetic-quantummechanical properties of the simplest topologically admissible field structures, based on quantized flux, relate Bohr- and muon-magneton to charges ±e (leptons), and ±e/3, ±2e/3, ±e/3 (quarks). Coaxial toroidal structures of pairs and triplets of quark fields characterize ordinary mesons and baryons. Also J/ψ, ? and jet structures fit into the concept of linkage of loops of quantized flux.     

Fourth generation of quarks and leptons

Permutation Symmetry sugests an intergeneration quark-lepton mass formulam _μ /m _τ /m _L =m _s /m _b /m _b′ =m _c /m _t /m _t′ . We consider several possibilities We consider several possibilities for the fourth generation masses.     

Signals of excited quarks and leptons

e⁺e^? annihilation to two photons (including beam polarization) and quark-antiquark annihilation to gluons are discussed as possible tools to investigate the existence (and handedness) of excited electrons and quarks. Properties of these particles can also be explored in eγ and ep colliders; production cross sections and the impact of these particles on structure functions are derived.     

Constituent models for quarks and leptons

Constituent models predicting several families of quarks and leptons are presented. They satisfy 't Hooft's anomaly conditions and a “principle of exclusion” introduced here. Some mechanisms for breaking GSW symmetry and generating masses for quarks and leptons consistent with the GIM mechanism are also given.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

Generations of massless composite quarks and leptons

We present a QCD-like composite model in which quarks, leptons and technifermions are three-body systems made out of three kinds of massless elementary fermions t, c and w, each carrying technicolor, color and weak gauge interactions, respectively. Discrete symmetries, remnants of the U(1)_A of the original lagrangian, are responsible for the masslessness of all the quarks and leptons and give the precise meaning of the generations. The model exhibits three generations for both quarks and leptons. Small but non-zero masses of the quarks and leptons are produced by the technicolor condensate of the composite technifermions, which thereby leads to the non-trivial Cabibbo mixing. Proton decays are all forbidden at the mass scale of the QCD-like theory.     

Four families of composite quarks and leptons

Four families of composite quarks and leptons, two standard and two non-standard, are found in a unique solution SU(3)_HC × SU(6)_L × SU(6)_R of a restricted 't Hooft anomaly-matching program. Testable predictions emerge, such as prohibition of μ → eγ, zero charge asymmetry in e⁺e^? → τ⁺τ^? in contrast to e⁺e^? → μ⁺μ^?, and a rich new hadron spectrum masses around M_W. A minimal set of spectator fermions contains color-singlet objects with fractional quark-like charges.     

A composite model of leptons and quarks

A heuristic model is presented, treating leptons and quarks as composites of spin $\text{1}\text{2}$ fields with charges 0, $\text{±}\text{e}\text{3}$. A distinguishability assumption leads to the emergence of three quark colors. The model is extended to consideration of the force-mediating bosons.     

Composite quarks and leptons and horizontal symmetries

We describe models of composite quarks and leptons in which an explicit generation quantum number is carried by one of the preons. We find several possible solutions for the subcolor and the horizontal groups.     

Composite quarks and leptons in supersymmetric grand unification

Chirality under SUSY-GUT is suggested as a sufficient condition for composites to be massless, in addition to the necessary anomaly matching á la 't Hooft. This results in a very stringent set of self-consistency requirements, which dictates also the number and structure of the generations. As an illustration I present an [SU(3)]³×[SUSY] model. It involves three generations (2 light + 1 heavy) and some other realistic features.     

Mass spectral condition for leptons and quarks

Consideration is given to the mass spectral conditiona(a,_m)a =a _m, wherea is the annihilation operator forQ=–1 states in the Hilbert space of leptons and quarks anda _m is the commutator resolvent ofa with respect tom. It is observed that this spectral condition, which simply requires a to be a congruent automorph ofa _m , implies that the third-, fourth-, and fifth-generationQ=-1 leptons have the masses 1788.03 MeV, 42.1649 GeV, and 1.33422 TeV, respectively. With the assumption that the mass spectral condition also holds forQ=0 states in the Hilbert space, one obtains new theoretical upper and lower bounds on the neutrino masses.     

Constraints on composite models of quarks and leptons

The previously noted difficulty of obtaining Dirac magnetic moments in composite models is combined with the observation that a “light” bound fermion state with a small size must have the Dirac moment in a renormalizable theory since its anomalous moment is determined by its excitation spectrum. New constraints on composite models are given, including the decoupling of low-lying excitations and the “superconfinement” condition that creation of virtual electron-positron pairs by the superstrong gluons responsible for binding the constituents of the electron must be strictly forbidden in photon-electron scattering.     

QDD—a model of quarks and leptons

An economical scheme for composite quarks and leptons is suggested. The basic vector particles of the theory are, like gluons, confined and the intermediate vector bosons are also composites. A possible “reason” for the existence of families emerges.     

Quarks and leptons as composite goldstone fermions

A dynamical scheme for composite quarks and leptons is proposed in which the observed fermions are Goldstone particles of spontaneously broken supersymmetry. Their residual interactions are described by a minimal effective lagrangian which invokes a non-linear realization of sypersymmetry. Possible experimental consequences are studied and it is found that the most conspicuous signature of this scheme would be a dramatic increase in the lepton pair production in hadronic collisions, particularly in $\text{pp}$ scattering, at high energy.     

The magnetic moment of composite leptons and quarks

We show that for a composite fermion of sufficiently small radius, the magnetic moment approaches the Dirac value corresponding to the overall charge and mass, regardless of the constituent values. This resolves a recently suggested difficulty in composite models of leptons and quarks.     

Scales of mass generation for quarks, leptons, and majorana neutrinos

We study 2-->n inelastic fermion-(anti)fermion scattering into multiple longitudinal weak gauge bosons and derive universal upper bounds on the scales of fermion mass generation by imposing unitarity of the S matrix. We place new upper limits on the scales of fermion mass generation, independent of the electroweak symmetry breaking scale. Strikingly, we find that the strongest 2-->n limits fall in a narrow range, 3-170 TeV (with n=2-24), depending on the observed fermion masses.